
Re: Surface geodesics
Posted:
Jan 20, 2014 3:31 AM


On Mon, 20 Jan 2014, ?~B?XPOSITO wrote:
> Thanks a lot for your reply. I haven't yet thought about it, but I would like > to ask you, if this is not a silly question, what are the symbols \/ and R.
\/ union; /\ intersection; R the set of reals ordered by magnitude with the open interval topology.
Another example is a tube with it's axis bent into a helix.
> > > Can somebody provide an example of a connected surface containing a > > > nonplane> geodesic, apart from those surfaces contained in the plane > > > or the sphere? Does such a surface even exist? > > > > Yes. > > ( (x,y,z}  x^2 + y^2 = 1, z in [1,1] } > > . . \/ Rx[2,2]x{1} \/ [2,2]xRx{1} > > . .  { (x,y)  x^2 + y^2 < 1 }x{1,1}. > > > > A ribbon 3 ft by 4 in. twisted lengthwise 2 rotations. > > > > > > >

